The Central European Watershed divides the Rhine-Main catchment and the Danube catchment. In the Early Medieval period, when ships were important means of transportation, Charlemagne decided to link both catchments by the construction of a canal connecting the Schwabian Rezat and the Altmühl rivers. The artificial waterway would provide a continuous inland navigation route from the North Sea to the Black Sea. The shortcut is known as Fossa Carolina and represents one of the most important Early Medieval engineering achievements in Europe. Despite the important geostrategic relevance of the construction it is not clarified whether the canal was actually used as a navigation waterway. We present new geophysical data and in situ findings from the trench fills that prove for the first time a total length of the constructed Carolingian canal of at least 2300 metres. We have evidence for a conceptual width of the artificial water course between 5 and 6 metres and a water depth of at least 60 to 80 cm. This allows a crossing way passage of Carolingian cargo scows with a payload of several tons. There is strong evidence for clayey to silty layers in the trench fills which reveal suspension load limited stillwater deposition and, therefore, the evidence of former Carolingian and post-Carolingian ponds. These findings are strongly supported by numerous sapropel layers within the trench fills. Our results presented in this study indicate an extraordinarily advanced construction level of the known course of the canal. Here, the excavated levels of Carolingian trench bottoms were generally sufficient for the efficient construction of stepped ponds and prove a final concept for a summit canal. We have evidence for the artificial Carolingian dislocation of the watershed and assume a sophisticated Early Medieval hydrological engineering concept for supplying the summit of the canal with adequate water.

The operating principle of traveling-wave parametric amplifiers is typically understood in terms of the standard coupled mode theory, which describes the evolution of forward propagating waves without any reflections, i.e., for perfect impedance matching. However, in practice, superconducting microwave amplifiers are unmatched nonlinear finite-length devices, where the reflecting waves undergo complex parametric processes, not described by the standard coupled mode theory. Here, we present an analytical solution for the TWPA gain, which includes the interaction of reflected waves. These reflections result in corrections to the well-known results of the standard coupled mode theory, which are obtained for both three-wave and four-wave mixing processes. Due to these reflections, the gain is enhanced and unwanted nonlinear phase modulations are suppressed. Predictions of the model are experimentally demonstrated on two types of unmatched TWPA, based on coplanar waveguides with a central wire consisting of (i) a high kinetic inductance superconductor, and (ii) an array of 2000 Josephson junctions.

We describe a dual current source designed to provide static flux biases for a superconducting qubit and for the Superconducting QUantum Interference Device $(\mathrm{SQUID})$ which measures the qubit state. The source combines digitally programmable potentiometers with a stabilized voltage source. Each channel has a maximum output of $\text{±1\hspace{0.5em}}\mathrm{mA}$ , and can be adjusted with an accuracy of about $\text{±1\hspace{0.5em}}\mathrm{nA}$ . Both current supplies are fully computer controlled and designed not to inject digital noise into the quantum bit and $\mathrm{SQUID}$ during manipulation and measurement of the flux. For a $\text{275\hspace{0.5em}μ}\mathrm{A}$ setting, the measured noise current is 2.6 parts per million (ppm) rms, in a bandwidth of $\text{0.0017–10\hspace{0.5em}}\mathrm{Hz}$ , from which we estimate dephasing times of hundreds of nanoseconds in the particular case of our own qubit design. By resetting the current every $\text{10\hspace{0.5em}}\min$ , we are able to reduce the drift to no more than $\text{5\hspace{0.5em}}\mathrm{ppm}$ at a current of $\text{750\hspace{0.5em}μ}\mathrm{A}$ over a period of 3 days. The current source has been implemented without thermal regulation inside a radiofrequency-shielding room, and is used routinely in our quantum coherence experiments.

The Early Medieval Fossa Carolina is the first hydro-engineering construction that bridges the Central European Watershed. The canal was built in 792/793 AD on order of Charlemagne and should connect the drainage systems of the Rhine-Main catchment and the Danube catchment. In this study, we show for the first time, the integration of Airborne LiDAR (Light Detection and Ranging) and geoarchaeological subsurface datasets with the aim to create a 3D-model of Charlemagne’s summit canal. We used a purged Digital Terrain Model that reflects the pre-modern topography. The geometries of buried canal cross-sections are derived from three archaeological excavations and four high-resolution direct push sensing transects. By means of extensive core data, we interpolate the trench bottom and adjacent edges along the entire canal course. As a result, we are able to create a 3D-model that reflects the maximum construction depth of the Carolingian canal and calculate an excavation volume of approx. 297,000 m³. Additionally, we compute the volume of the present dam remnants by Airborne LiDAR data. Surprisingly, the volume of the dam remnants reveals only 120,000 m³ and is much smaller than the computed Carolingian excavation volume. The difference reflects the erosion and anthropogenic overprint since the 8th century AD.